A062142 Fourth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

1, 28, 560, 10080, 176400, 3104640, 55883520, 1037836800, 19978358400, 399567168000, 8310997094400, 179819755315200, 4045944494592000, 94612855873536000, 2297740785500160000, 57903067794604032000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Examples

			a(3) = (3+3)!*binomial(3+6,6)/3! = (720*84)/6 = 10080. - _Indranil Ghosh_, Feb 23 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..400
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062137, A062141.

Programs

Magma

[Factorial(n+3)*Binomial(n+6,6)/6: n in [0..20]]; // G. C. Greubel, May 12 2018

Mathematica

Table[(n+3)!*Binomial[n+6,6]/3!,{n,0,15}] (* Indranil Ghosh, Feb 23 2017 *)

PARI

a(n) =(n+3)!*binomial(n+6,6)/3! \\ Indranil Ghosh, Feb 23 2017

Python

import math
f=math.factorial
def C(n,r):
    return f(n)/f(r)/f(n-r)
def A062142(n):return f(n+3)*C(n+6,6)/f(3) # Indranil Ghosh, Feb 23 2017

Sage

[binomial(n,6)*factorial(n-3)/factorial(3) for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009

Formula

a(n) = (n+3)!*binomial(n+6, 6)/3!; e.g.f.: (1 + 18*x + 45*x^2 + 20*x^3)/(1-x)^10.

If we define f(n,i,x) = Sum_{k=1..n} Sum_{j=1..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i)*x^(k-j), then a(n-3) = (-1)^(n-1)*f(n,3,-7), (n>=3). - Milan Janjic, Mar 01 2009